South Africa's president, Jacob Zuma, is today facing one of the biggest tests of his presidency as tens of thousands of striking workers took to the streets and relations with his union backers neared breaking point.

The Congress of South African Trade Unions (Cosatu) warned that its historic alliance with Zuma's governing African National Congress (ANC) had reached a critical low.

Zwelinzima Vavi, secretary general of Cosatu, said government corruption had derailed the alliance's agenda. "The emergence of a 'new tendency' focused on taking over the ANC and using access to the state for a selfish accumulation agenda disrupted the emerging unity of purpose, which has led to a paralysis in both the alliance and government," he said.

"The alliance is unable to convene an alliance summit for fear of an implosion as a result of fundamental differences on the question of where the power lies."

Vavi condemned a lack of decisive leadership. "The alliance is again dysfunctional; the centre cannot hold," he said.

Cosatu's role as potential kingmaker was evident in 2007 when, having lost patience with the then president, Thabo Mbeki, it threw its weight behind Zuma. Some critics say that Zuma's promises to the labour movement and others are now coming home to roost.

Vavi recently told an angry crowd demonstrating over low pay that Zuma earns more than R2.2m (£193,000) a year. "He has blood like we have blood," he said. "He has a big family like we do. He has children to feed like we do. Our needs are the same."

Analysts said Cosatu, which forged ties with the ANC in the struggle to end apartheid, would have too much to lose from a split. But William Gumede, author of Thabo Mbeki and the Battle for the Soul of the ANC, warned that the political fallout could be damaging.

"It's a big moment for the alliance," he said. "These are some of the people who brought Zuma to power. As this strike goes on, the same people are potentially talking about getting Zuma out.

"Zuma has wanted to please everybody but in this kind of situation you can't please everybody. If he chooses one side then he loses the other. The strike could be a tipping point."

Cosatu, which says it has 2m members, has warned of a "total shutdown" of the South African economy next week if the government does not meet its demand for an 8.6% wage rise and 1,000 rand (£88) monthly housing allowance.

Cosatu said it had filed seven-day strike notices for members to join the state workers in a stoppage that would then hit mining and manufacturing. Police and army medics could also join in, bringing the country to a standstill.

In a major show of strength today, thousands of workers marched through cities waving placards, wearing union T-shirts and singing apartheid-era protest songs. The strike by about 1.3 million state employees is now in its eighth day and has shut schools and crippled hospitals.

Frustration with government was palpable in a country where half of young black men are unemployed. In Johannesburg workers danced, blew vuvuzelas, sang anti-Zuma songs and chanted: "We are going, we are going to Luthuli House [the ANC headquarters]." In Bloemfontein, thousands marched peacefully through the streets, carrying banners such as: "We behaved during the World Cup. Now reward us with 8.6%."

The National Aids Council expressed fears about the effects on HIV-positive people, saying it had received reports of patients struggling to get access to medicine.

The Health Professions Council of South Africa condemned "shocking effects" on patient welfare. Marella O'Reilly, its acting registrar and chief executive, said: "The dismal picture portrayed in our public hospitals as a result of the strike is one of disgrace, embarrassment and failure."

The South African army has sent doctors and other personnel to help at 47 hospitals across the country. But the SA National Defence Union is now considering a stoppage in solidarity with public servants.

The police union has also said its members will down tools on Saturday. But police management obtained a court order barring police from striking and said officers who joined the protests could be fired.

There have been reports of teachers being abused for crossing school picket lines, and even some children suffering intimidation. Exams have been postponed in some provinces.

Steven Friedman, director of the Centre for the Study of Democracy, said the unions were disappointed with Zuma. "The strike illustrates that, from the perspective of the trade unions, the government they are dealing with now is exactly the same as before Zuma was elected. The Zuma presidency was held up to Cosatu as more pro-labour. But it hasn't been and it will be interesting to see how union leaders react.

"Will the unions campaign against Zuma in two years' time? There are two questions. Do they have the votes to do it? Probably not. And who would they put in his place? There is no obvious candidate."

Friedman also ruled out a split between the ANC and Cosatu. "There's not much incentive on either side to pull the alliance apart. I guess that the ANC and Cosatu have had their honeymoon and now this is the death knell. There will be a more adversarial relationship, but that's nothing new."